The Visual Computer

, Volume 22, Issue 9–11, pp 604–611 | Cite as

Surface mosaics

  • Yu-Kun Lai
  • Shi-Min HuEmail author
  • Ralph R. Martin
Special Issue Paper


This paper considers the problem of placing mosaic tiles on a surface to produce a surface mosaic. We assume that the user specifies a mesh model, the size of the tiles and the amount of grout, and, optionally, a few control vectors at key locations on the surface indicating the preferred tile orientation at these points. From these inputs, we place equal-sized rectangular tiles over the mesh such as to almost cover it, with controlled orientation. The alignment of the tiles follows a vector field which is interpolated over the surface from the control vectors and also forced into alignment with any sharp creases, open boundaries, and boundaries between regions of different colors. Our method efficiently solves the problem by posing it as globally optimizing a spring-like energy in the Manhattan metric, using overlapping local parameterizations. We demonstrate the effectiveness of our algorithm with various examples.


Surface mosaics Particle optimization Manhattan metric Overlapping local parameterizations 


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  1. 1.
    Alliez, P., Cohen-Steiner, D., Devillers, O., Lévy, B., Desbrun, M.: Anisotropic polygonal remeshing. ACM Trans. Graph. 22(3), 485–493 (2003)CrossRefGoogle Scholar
  2. 2.
    Alliez, P., de Verdiere, E.C., Devillers, O., Isenburg, M.: Isotropic surface remeshing. In: Proc. Shape Modeling International Conference, pp. 49–58 (2003)Google Scholar
  3. 3.
    Botsch, M., Kobbelt, L.: Resampling feature and blend regions in polygonal meshes for surface anti-aliasing. Comput. Graph. Forum 20(3), 402–410 (2001)CrossRefGoogle Scholar
  4. 4.
    Cohen-Steiner, D., Morvan, J.M.: Curve and surface reconstruction: Restricted delaunay triangulations and normal cycle. In: Proc. 19th Annual ACM Symposium on Computational Geometry, pp. 312–321 (2003)Google Scholar
  5. 5.
    Elber, G., Wolberg, G.: Rendering traditional mosaics. Visual Comput. 19, 67–78 (2003)CrossRefGoogle Scholar
  6. 6.
    Finkelstein, A., Range, M.: Image mosaics. In: R.D. Hersch, J. André, H. Brown (eds.) Proc. 7th International Conference on Electronic Publishing, pp. 11–22 (1998)Google Scholar
  7. 7.
    Floater, M.S., Hormann, K.: Surface parameterization: a tutorial and survey. In: Advances in Multiresolution for Geometric Modelling, pp. 157–186. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  8. 8.
    Hausner, A.: Simulating decorative mosaics. In: Proc. ACM SIGGRAPH, pp. 573–580 (2001)Google Scholar
  9. 9.
    Kaplan, C.S., Salesin, D.H.: Escherization. In: Proc. ACM SIGGRAPH, pp. 499–510 (2000)Google Scholar
  10. 10.
    Kim, J., Pellacini, F.: Jigsaw image mosaics. ACM Trans. Graph. 21(3), 657–664 (2002)Google Scholar
  11. 11.
    Klein, A.W., Grant, T., Finkelstein, A., Cohen, M.F.: Video mosaics. In: Second International Symposium on Non Photorealistic Rendering, pp. 21–28 (2002)Google Scholar
  12. 12.
    Marinov, M., Kobbelt, L.: Direct anisotropic quad-dominant remeshing. In: Proc. Pacific Graphics, pp. 207–216 (2004)Google Scholar
  13. 13.
    Mount, D., Arya, S.: ANN: A library for approximate nearest neighbor searching, ver 1.1, http:∼mount/ANN (2005)Google Scholar
  14. 14.
    Ray, N., Li, W.C., Lévy, B., Sheffer, A., Alliez, P.: Periodic global parameterization. ACM Trans. Graph. (to appear) (2006)Google Scholar
  15. 15.
    Silvers, R., Hawley, M.: Photomosaics. Henry Holt, New York (1997)Google Scholar
  16. 16.
    Surazhsky, V., Gotsman, C.: Explicit surface remeshing. In: Proc. Eurographics Symposium on Geometry Processing, pp. 17–28. Aachen, Germany (2003)Google Scholar
  17. 17.
    Szeliski, R., Tonnesen, D.: Surface modeling with oriented particle systems. In: Proc. SIGGRAPH, pp. 185–194 (1992)Google Scholar
  18. 18.
    Turk, G.: Texture synthesis on surfaces. In: Proc. ACM SIGGRAPH, pp. 347–354 (2001)Google Scholar
  19. 19.
    Wei, L.Y., Levoy, M.: Texture synthesis over arbitrary manifolds. In: Proc. ACM SIGGRAPH, pp. 355–360 (2001)Google Scholar
  20. 20.
    Witkin, A., Heckbert, P.: Using particles to sample and control implicit surfaces. In: Proc. ACM SIGGRAPH, pp. 269–277 (1994)Google Scholar
  21. 21.
    Yang, Y.L., Lai, Y.K., Hu, S.M., Pottmann, H.: Robust principal curvatures on multiple scales. In: K. Polthier, A. Sheffer (eds.) Proc. Eurographics Symposium on Geometry Processing, pp. 223–226. Eurographics Association (2006)Google Scholar

Copyright information

© Springer-Verlag 2006

Authors and Affiliations

  1. 1.Tsinghua UniversityBeijingChina
  2. 2.Cardiff UniversityCardiffUK

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